Title: Equidistribution of periodic points for endomorphisms of P^k

Abstract: Equidistribution phenomena are naturally present in several branches of mathemematics. The usual picture is that a sequence of points on a space X defined in some natural way always converge to a given limit distribution (a probability measure on X). In the case of dynamical systems, two natural choices are given by the iterated  pre-images of a given point or periodic points of period tending to infinity.

In the holomorphic world,  it is known since the works of Lyubich in dimension 1 and Briend-Duval in any dimension that the periodic points of a holomorphic endomorphism of P^k equidisitribute towards its equilibrium measure.  Arithmetic versions also exist (Ullmo-Zhang,  Baker Rumely, Favre- Rivera-Letelier, Chamber-Loir, Yuan-Zhang, etc).

In this talk, I will discuss  results concerning the speed of convergence in the above theorems in the holomorphic category. This is a joint work with H. de Thélin and T.-C. Dinh.

Seminarraum 05.002, Spiegelgasse 5